N91- 17733 NASCAP/LEO CALCULATIONS OF CURRENT COLLECTION M. J. Mandell, I. Katz, V. A. Davis, R. A. Kuharski S-CUBED, A Division of Maxwell Laboratories, Inc. P. O. Box 1620, La Jolla, California 92038 _b__. NASCAP/LEO is a 3-dimensional computer code for calculating the interaction of a high-voltage spacecraft with the cold dense plasma found in Low Earth Orbit. Although based on a cubic grid structure, NASCAP/LEO accepts object definition input from standard CAD programs so that a model may be correctly proportioned and important features resolved. The potential around the model is calculated by solving the finite element formulation of Poisson's equation with an analytic space charge function. Five previously published NASCAP/LEO calculations for three ground test experiments and two space flight experiments are presented. The three ground test experiments are a large simulated panel, a simulated pinhole, and a 2-slit experiment with overlapping sheaths. The two space flight experiments are a solar panel biased up to I000 volts, and a rocket-mounted sphere biased up to 46 kilovolts. In all cases, we find good agreement between calculation and measurement. Introduction This report is an expanded version of a poster presenta- tion made at the "Workshop on Current Collection from Space Plasmas," Huntsville, Alabama, April 24-25, 1989. The objective of this document is to summarize the capabilities and the physical and numerical basis of the NASCAP/LEO computer code. NASCAP/LEO is capable of calculating the potential and sheath structure around a geometrically and electrically complex spacecraft immersed in a plasma, and the plasma currents collected by the surfaces of such an object. We present here five previously published case studies of NASCAP/LEO simulations of experiments studying interactions of charged surfaces with a plasma representative of Low Earth Orbit. Three of the experiments were performed under ground test conditions, and two were for actual space flights. As the first four cases were done with an older version of NASCAP/LEO that required that objects be made of cubes, these objects were redefined and a few calculations performed to illustrate NASCAP/LEO's present capabilities. All the new calculations agreed with the previously published results. 334 https://ntrs.nasa.gov/search.jsp?R=19910008420 2020-06-22T05:24:29+00:00Z
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N91- 17733NASCAP/LEO CALCULATIONS OF CURRENT COLLECTION
M. J. Mandell, I. Katz, V. A. Davis, R. A. Kuharski
S-CUBED, A Division of Maxwell Laboratories, Inc.
P. O. Box 1620, La Jolla, California 92038
_b__. NASCAP/LEO is a 3-dimensional computer code for
calculating the interaction of a high-voltage spacecraft with
the cold dense plasma found in Low Earth Orbit. Although
based on a cubic grid structure, NASCAP/LEO accepts object
definition input from standard CAD programs so that a model
may be correctly proportioned and important features
resolved. The potential around the model is calculated by
solving the finite element formulation of Poisson's equation
with an analytic space charge function.
Five previously published NASCAP/LEO calculations for
three ground test experiments and two space flight
experiments are presented. The three ground test experiments
are a large simulated panel, a simulated pinhole, and a
2-slit experiment with overlapping sheaths. The two space
flight experiments are a solar panel biased up to I000 volts,
and a rocket-mounted sphere biased up to 46 kilovolts. In
all cases, we find good agreement between calculation and
measurement.
Introduction
This report is an expanded version of a poster presenta-
tion made at the "Workshop on Current Collection from Space
Plasmas," Huntsville, Alabama, April 24-25, 1989. The
objective of this document is to summarize the capabilities
and the physical and numerical basis of the NASCAP/LEO
computer code. NASCAP/LEO is capable of calculating the
potential and sheath structure around a geometrically and
electrically complex spacecraft immersed in a plasma, and
the plasma currents collected by the surfaces of such an
object.
We present here five previously published case studies of
NASCAP/LEO simulations of experiments studying interactions
of charged surfaces with a plasma representative of Low
Earth Orbit. Three of the experiments were performed under
ground test conditions, and two were for actual space
flights. As the first four cases were done with an older
version of NASCAP/LEO that required that objects be made of
cubes, these objects were redefined and a few calculations
performed to illustrate NASCAP/LEO's present capabilities.
All the new calculations agreed with the previously
NASCAP/LEOfeatures the ability to accept a generalgeometrical description of the spacecraft or test object.The spacecraft is defined as a finite element surface modelusing a standard CAD finite element generator such asPatran (a) or EMRC(b) Display-II. An interface code readsthe "neutral file" output by the finite element generatorand places the object in a cubic grid. Variable surfaceresolution is naturally achieved in the finite elementgenerator; locally enhanced spatial resolution is availablevia directive to the interface code. The object may bedefined with correct angles and proportions independent ofthe cubic grid resolution.
NASCAP/LEOis designed to calculate space potentials inthe regime where the applied voltages are large compared tothe plasma temperature, and the Debye length is comparableto, or less than, the code resolution. A local space chargeformulation takes account of plasma screening andacceleration and convergence of charged particles such thatthe Langmuir-Blodgett result will be reproduced for aspherical sheath. Currents flowing from the sheath to theobject are calculated taking into account ram-wake andmagnetic field effects.
NASCAP/LEOalso has specialized modules to calculatespacecraft floating potentials, surface charging, meanpotential of a solar array surface, parasitic power loss ofa solar-voltaic power system, and hydrodynamic ion flowabout a spacecraft.
Physical and Numerical Basis of NASCAP/LEO
NASCAP/LEOis a 3-dimensional computer code that cancalculate self-consistently electrostatic potentialssurrounding a charged object, plasma currents incident onobject surfaces, and object surface potentials for plasmaconditions appropriate to low earth orbit.
The electrostatic potential, _, about the object is
determined by solving Poisson's equation
-V20 = pl_ (i)
subject to fixed potential or fixed electric field boundary
conditions at object surfaces. (These boundary conditions
may be set by the user, or by other modules of NASCAP/LEO.)
The space charge, p, appearing in Poisson's equation is
approximated as a nonlinear analytic function of the plasma
properties and the local potential and electric field. The
function used is
(a) Patran is a trademark of PDA Engineering, Costa Mesa, CA.
(b) Engineering Mechanics Research Corporation, Troy, MI.
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p(¢,E)/eO = _ (¢112)
x [I+C (¢, E)_]
x [1+(4tc)]121¢181312]-1 (2)
where the first factor represents linear screening with
Debye length k, the second represents increase in density
due to trajectory convergence (where the convergence factor
C(_,E) is a function of local field and potential calculated
to give the correct answer for a Langmuir-Blodgett spherical
sheath), and the third represents decrease in density due to
particle acceleration, with 8 being the plasma temperature
[eV]. An algorithm is included to account for ram-wake
effects in the neutral particle approximation.
NASCAP/LEO solves the variational form of Poisson's
equation
(3)
using the finite element method and a conjugate gradient
technique for sparse linear equations. After each solution
of the linear equations, the nonlinear space charge is
linearized about the current solution, and the new equations
solved. This process is continued until the solution is
deemed sufficiently near a fixed point.
The finite element method works well for this problem
because most of space is filled with trilinear "empty"
elements. "Stiffness matrices" for those elements
containing surfaces are constructed numerically. The
potential solver allows "nested outer grids" in order to
include a large volume of space, and "subdivided inner
grids" to achieve locally enhanced resolution where needed.
NASCAP/LEO calculates currents to a charged object using
the "sharp sheath edge" approximation. The "sharp sheath
edge" is a specified equipotential surface (usually ±81n2) .
Macroparticles representing ion and/or electron currents are
generated for each element of sheath area, taking ram-wake
effects into account. These macroparticles are tracked in
the electric fields resulting from the Poisson solution, and
user-specified magnetic fields, to determine where (or
whether) they strike the object.
Potentials of insulating surfaces are calculated to
achieve current balance among the incident (sheath and
thermal) ions and electrons, and the secondary electrons.
For insulators near high positive voltage surfaces, we use an
electric field boundary condition which represents
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equilibrium between incident electrons and transport ofsecondary electrons along the surface. This boundarycondition is given by
g,n = [4 <£> Y V,EII ]I/2 (4)
where <£> is the mean energy of secondary electrons and Y is
the secondary yield for primary electrons with energy equal
to the surface potential.
A solar array surface is an important example of a complex
surface that is a mosaic of dielectric (coverslips) and
conductor (interconnects). Because of the obvious importance
of solar arrays on spacecraft, we have developed an
algorithm, based on equation (4), to calculate self-
consistently the mean potential and mean electric field for
a periodic surface. This algorithm, which takes advantage
of the periodic structure of solar arrays, is discussedfurther in section 6 below.
Example I: Simulated Solar Panel (1980) (Katz et al., 1981)
The first NASCAP/LEO paper ever published reported
simulation of measurements by McCoy and Konradi (1979) of
current collection by a 10-meter long "panel" exposed to an
argon plasma in the large vacuum chamber at Johnson Space
Center. The "panel" was actually a conducting strip mounted
on a plastic frame. The strip could be held at fixed
constant potential or could maintain a linear potential
gradient along its length.
Figure 1 shows the NASCAP/LEO model of the panel. This
model was constructed using EMRC Display-II. Note the
variable resolution across the width of the panel, giving
good resolution of the metal-plastic interface. Variable
resolution is also used lengthwise near the ends. Figure 2
shows the same panel with linear bias (in ten steps) from
zero to -4,800 volts.
Figure 3 shows the plasma potentials around the panel for
the bias shown in figure 2. The plasma conditions used in
the calculation were plasma density n = 1.3 x 106 cm -3, and
plasma temperature e = 2.3 eV. The sheath shape is in
agreement with what was visually observed. The primary grid
unit is 0.333 meters. Note the locally enhanced resolution
used near the panel surface.
The calculation also gives the current density on the
panel surface, which is strongly enhanced at the high voltage
end. The total current collected was 26 milliamperes, which
compares well with a measurement of "slightly under"
20 milliamperes when the panel was biased from zero to
-4,000 volts.
337
Example 2: Simulated Pinhole (1983) (Mandell and Katz, 1983)
It is well accepted that a small, positively biased
conducting surface can collect current out of proportion to
its size if surrounded by dielectric material. This is
because secondary electron emission facilitates the spread
of high positive voltage from the conductor onto the
surrounding insulator. NASCAP/LEO models this phenomenon by
requiring current balance between the incident electron
current and the divergence of the current carried by the
secondary electron layer. As the latter is proportional tothe incident electron current and a strong function of the
normal electric field at the surface, the potential at the
dielectric surface is determined by imposing the boundary
condition of a small (but nonzero) outward pointing electric
field, whose value is given by equation (4).
Experiments performed by Gabriel et al. (1983) made an
excellent test of the treatment of this phenomenon by
NASCAP/LEO. The experiment fixture was kapton-covered except
for a circular region of diameter either 1.27 cm or 0.64 cm.
The experimenters measured the potentials in the plasma along
the "pinhole" axis. For the smaller pinhole, the collected
current was measured.
Figure 4 shows the surface potentials on the NASCAP/LEO
model of the fixture with the larger pinhole. The model was
constructed using EMRC Display-II, and has good resolution
in the region surrounding the pinhole. (A similar model was
constructed for the smaller pinhole.) The pinhole was biased
to +458 volts in a plasma with n = 5.8 x 104 cm -3, 8 = 4 eV.
The spread of high potential onto the insulator is clearly
seen.
Figure 5 shows the potentials in space above the pinhole
for the same case. The NASCAP/LEO results are compared with
experiment in figure 6, which is taken from the original
paper (Mandell and Katz, 1983).
For the smaller pinhole, the experimenters measured a
collected current of 4 _A when the pinhole was biased to
458 volts in a plasma with n = 2.5 x 104 cm -3, 8 = 5.3 eV.
This value approaches the orbit-limited value of 4.2 _A, and
is far in excess of the planar current estimate of 0.05 _A.
The collection of orbit-limited current is consistent with a
zero electric field boundary condition on the dielectric.
The NASCAP/LEO calculated current is 2.4 _A.
Example 3: Overlapping Sheaths (1987) (Davis et al., 1988)
A related experiment was performed by Carruth. (1987).
Rather than the pinhole geometry, Carruth measured collected
current and plasma potential for the more complex geometry
of two parallel slits. Carruth used relatively low voltages
338
so as to avoid "snapover". (At higher voltages, a sharp
increase in current, indicating snapover, was observed.)
Figure 7 shows the NASCAP/LEO model of Carruth's
experiment with biases of 128 and 328 volts on the slits.
Once again, this model was constructed using EMRC Display-II.
Though it is not apparent from the figure, the model was
constructed such that the current collected by the central
4.2 cm of each slit could be calculated, the same quantity
measured in the experiment. Figure 8 shows a sheath contour
plot for plasma conditions n = 2 x 106 cm -3, 8= 2 eV. (The
primary grid spacing used for this calculation was 1.429 cm.)
The figure shows that the sheaths of the two slits do indeed
overlap. The calculated potentials agree well with the
experimental measurements.
Figure 9 [taken from the original paper (Davis et al.,
1988)] shows the current collected by each of the two slits
when one is held at I00 volts and the potential of the other
is varied. Agreement between experiment and calculation isexcellent.
Example 4: PIX-II Flight Experiment (1983)
(Mandell et al., 1986)
PIX-II (Grier, 1985) was an orbital experiment designed to
measure the interaction of a high-voltage (up to
±i,000 volts) solar array with the plasma environment. The
instrumentation consisted of a 2,000 cm 2 passive solar arraywhose interconnects could be biased relative to the rocket
ground, a Langmuir probe, and a hot-wire neutralizer. The
results showed that current collection was enhanced by the
"snapover" effect at positive biases over a few hundred
volts, and that arcing occurred at negative biases as low as250 volts.
In modeling the PIX-II experiment, it rapidly became
apparent that it was not possible to resolve in detail a
surface consisting of 2 cm x 2 cm solar cells with 0.i cm
interconnects. Strategies such as lumping the many inter-
connects together into a few surface zones gave a grossly
inadequate representation of the surface. Therefore, taking
into account that a solar array surface is a periodic
structure, an analytic representation of this surface was
developed. The physical content of this solar array surface
model is that a dielectric in a cold plasma can achieve
current balance either (i) at negative potential such that
ion and electron currents balance, or (2) at small, positive
electric field (given by equation (4)), provided that the
resulting potential is high enough to produce secondary
electron yield greater than unity. When the coverslips are
in the latter condition due to the presence of high-voltage
interconnects, the coverslip potential profile must be such
that the positive (electron-attracting) mean electric field
339
must be approximately canceled by the spatially periodiccomponents. These ideas lead to a formulation that cal-culates the mean potential of the surface self-consistentlywith the mean electric field returned from NASCAP/LEO'sPoisson solver. Its parameters include the cell size,interconnect size, and coverslip material properties.(Mathematical details may be found in Mandell et al., 1986.)Thus NASCAP/LEOis capable of predicting the "snapover" (orpartial snapover) of the coverslips in response to highpositive interconnect potentials, without explicitlyresolving the coverslips and interconnects.
Figure I0 shows the NASCAP/LEOmodel of PIX-II, con-structed using EMRCDisplay-II. This model is not baseddirectly on the PIX-II rocket, but rather on the originalNASCAP/LEOmodel of PIX-II. It differs from the originalmodel in that the rocket is round rather than square, andthat the change in resolution approaching the experimenttakes place smoothly rather than suddenly.
Figure II shows the surface potentials on the experiment
with the interconnects biased to 1,000 volts. Most of the
solar cells were calculated to have mean potential in the
range of 700-850 volts. For this case, the rocket structure
ground was taken to be at -4 volts, and the interconnects
comprised 5 percent of the cell area. Thus, we infer a mean
coverslip potential of about 150-300 volts below the
interconnect potential.
Figure 12 shows the current collected by the solar array
as a function of bias voltage. (This figure is taken from
the original publication.) The calculated values are in
general agreement with the measurements. The calculation
exhibits a sharper snapover at lower potential than was
measured because calculations were done in a manner which
tends to favor the bistable snapped-over state, while the
experiment was done by continuously increasing the bias which
tends to suppress the snapover.
Example 5: SPEAR I Rocket Experiment (1987)
(Katz et al., 1989)
The SPEAR (Space Power Experiments Aboard Rockets) program
has as its objective the development of technology for
efficient design of very high voltage and current systems to
operate in the space environment. The SPEAR I experiment
consisted of two boom-mounted probes that could be biased
up to 46 kilovolts positive relative to the rocket body. It
was intended that the rocket body would maintain good
contact with the ambient plasma via a hollow cathode plasma
contactor. However, the contactor was defeated by a
mechanical malfunction, so that the rocket body became
negatively charged, and the experiment was far less
340
symmetric than planned. NASCAP/LEOproved the utility of ageneral 3-dimensional modeling capability to understandthe results of this nonsymmetric flight experiment.
Figure 13 shows the NASCAP/LEOmodel of SPEARI with a46 kilovolt bias on one sphere and the rocket body at itsfloating potential of -8 kilovolts. The model wasconstructed using Patran. Figure 14 is a sheath contourplot showing the asymmetric sheath formed by SPEARI underthe above bias conditions. The plasma conditions for thiscalculation were n = 1 x 105 cm-3 and 8 = 0.i eV. The primarygrid unit is 0.3 meters, and the resolution in the region ofthe spheres is 7.5 centimeters.
Because the sheath is not symmetric about the sphere,theoretical results about the role of magnetic field inlimiting currents to spheres cannot be directly applied.Figure 15 shows the trajectory of an electron in apotential similar to that shown. The electron ExB drifts
around the surface of the sheath until (unlike the symmetric
case) it enters a high electric field region and is
collected. Figure 16 shows the NASCAP/LEO calculated
electron current to the sphere and the secondary-electron-
enhanced ion current to the rocket as a function of rocket
potential. As the potential goes negative, the electron
current first increases due to loss of symmetry, then
decreases due to the ion-collecting sheath engulfing the
electron-collecting sheath. Figure 17 shows the excellent
agreement between the measured current and the NASCAP/LEO
calculation.
While NASCAP/LEO takes account of the effect of magnetic
fields on particle trajectories and thus collected currents,
it ignores the effect of magnetic fields on the space charge
and potential structure. For comparison, the POLAR code was
run for the one case above to achieve self-consistent
space-charge, potential, and current solutions in the
presence of the magnetic field. The differences found were
fairly insignificant.
Summary
NASCAP/LEO is a 3-dimensional computer code capable of
calculating sheath structure, surface potentials, and
current collection for a high-voltage object in a plasma.
The ability to accept object definition input from standard
CAD programs allows spacecraft or test object models to be
correctly proportioned with important features adequately
resolved. The cubic grid structure and the analytic space
charge representation, together with phenomenological models
for other relevant physical phenomena (such as snapover),
permit realistic calculations to be performed in modest
amounts of computer time.
34J
We have highlighted in this report five previouslypublished NASCAP/LEOcalculations. These examples show thatit is practical to perform calculations for nonsymmetric,3-dimensional, realistic problems. They also verify thatNASCAP/LEO results stand the test of direct comparison withmeasurement for both ground test and space flight conditions.
Acknowledgements. This work has been supported by
NASA/Lewis Research Center under contract NAS3-23881.
References
Katz, I., M. J. Mandell, G. W. Schnuelle, D. E. Parks, and
P. G. Steen, Plasma collection by high-voltage spacecraft
in low earth orbit, J. Spacecraft, 18, 79, 1981.
McCoy, J. E. and A. Konradi, Sheath effects observed on a
i0 meter high voltage panel in simulated low earth orbit,
Spacecraft Charging Technology-1978, NASA CP-2071, 341,
1979.
Mandell, M. J. and I. Katz, Potentials in a plasma over a
